Apparatus and method for providing a flow measurement compensated for entrained gas

ABSTRACT

A apparatus  10,110  is provided that measures the speed of sound and/or vortical disturbances propagating in a fluid or mixture having entrained gas/air to determine the gas volume fraction of the flow  12  propagating through a pipes and compensating or correcting the volumetric flow measurement for entrained air. The GVF meter includes and array of sensor disposed axially along the length of the pipe. The GVF measures the speed of sound propagating through the pipe and fluid to determine the gas volume fraction of the mixture using array processing. The GVF meter can be used with an electromagnetic meter and a consistency meter to compensate for volumetric flow rate and consistency measurement respective, to correct for errors due to entrained gas/air.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application is a continuation in part of U.S. patent applicationSer. No. 10/715,197, filed on Nov. 23, 2003, now abandoned which claimedthe benefit of U.S. Provisional Application No. 60/426,723, filed Nov.15, 2002; U.S. Provisional Application No. 60/441,395, filed Jan. 21,2003, U.S. Provisional Application No. 60/441,652, filed Jan. 22, 2003;U.S. Provisional Application No. 60/442,968, filed Jan. 27, 2003, U.S.Provisional Application No. 60/503,349, filed Sep. 16, 2003; and U.S.Provisional Application No. 60/518,171, filed Nov. 7, 2003, all of whichare incorporated herein by reference in their entirety.

TECHNICAL FIELD

This invention relates to an apparatus for measuring a flow havingentrained gas therein, and more particularly to an apparatus thatmeasures the speed of sound propagating through the flow to determinethe gas volume fraction of the gas in the process flow and compensatingthe output measurement of a flow meter (e.g., a volumetric flow meterand a consistency meter) for entrained gas.

BACKGROUND ART

The present invention provides an apparatus and method of measuringvolumetric flow rate and gas volume fraction in slurries used in thepaper and pulp industries and in other industries. Slurries commonlyused in the paper and pulp industry are mostly water and typicallycontain between 1% and 10% pulp content by mass. Monitoring the flowrate and consistency of the slurry can lead to improved quality andefficiency of the paper production process.

Processes run in the paper and pulp industry can often, eitherintentionally or unintentionally, entrain gas/air. Typically, thisentrained air results in measurement errors in process monitoringequipment such as volumetric flow measurements and consistency meters.

Industry estimates indicate that entrained air levels of 2–4% arecommon. Since most process flow monitors are unable to distinguishbetween air and liquid, interpreting their output as liquid flow rateswould result in a overestimate of the liquid by the volumetric flow rateof the air present at the measurement location. Similarly, for the voidfraction of the air within the pipe can cause errors in consistencymeasurements.

Thus, providing a method and apparatus for measuring entrained air inpaper and pulp slurries would provide several benefits. Firstly, itwould provide a means to screen the output of process instrumentation.Secondly, in addition to screening the measurements, an accuratemeasurement of the entrained air would provide a means to correct theoutput of volumetric flow meters and consistency meters. Thirdly,monitoring variations in the amount of entrained air in a given processcould be indicative of process anomalies, such a worn bushing orcavitating pumps and/or valves.

Multiphase process flow rate is a critical process control parameter forthe paper and pulp industry. Knowing the amounts of liquid, solids andentrained gases flowing in process lines is key to optimizing theoverall the papermaking process (Matula, 2000). Unfortunately,significant challenges remain in the achieving accurate, reliable, andeconomical monitoring of multiphase flow rates of paper and pulpslurries. Reliability challenges arise due the corrosive and erosiveproperties of the slurry. Accuracy challenges stem from the multiphasenature of the slurries. Economical challenges arise from the need toreduce total life time cost of flow measurement, consideringinstallation and maintenance costs in addition to the initial cost ofthe equipment.

Currently, there is an unmet need for multiphase flow measurement in thepaper and pulp industry. Real time flow measurement is typicalrestricted to monitoring the total volumetric flow rate in a processline without providing information on the composition of the processmixture. For example, electromagnetic flow meters are the most widelyused flow meters in the paper and pulp industry, however they provide noindication of presence of entrained air, with its presence resulting inan over prediction of the volumetric flow of process fluid by the amountof air entrained. Consistency meter provide a measurement of thepercentage of solids within the process, however this technology remainsmore of an art than a science. Furthermore, although entrained air isknown to have a large, often deleterious, impact on the paper makingprocess, instrumentation is currently not available to provide thismeasurement on a real time basis.

The present invention an accurate, reliable multiphase flow measurementin the paper and pulp industry.

In one embodiment of the present invention, the apparatus and methodimproves the determination of consistency of paper and pulp slurries.Consistency refers to the mass fraction of pulp contained in water andpulp slurries used in the paper making process. Consistency measurementsare critical in the optimization of the paper making process. Currently,many companies produce consistency meters employing various technologyto serve the paper and pulp industry. Unfortunately, accurate andreliable measurement of consistency remains an elusive objective.Typically, interpreting the output of a consistency meter in terms ofactual consistency is more of an art than a science.

Of the various types of consistency meters on the market, microwavebased meters may represent the best the solution for many applications.One such microwave-based consistency meter is manufactured by Toshiba.Microwave consistency meters essentially measure speed or velocity themicrowave signal propagates through the medium being measured. Forexample, the speed of the microwave signal through water isapproximately 0.1 time the speed of light in a vacuum (c), through airis approximately 1.0 times the speed of light in a vacuum, and throughfiber (or pulp) is approximately 0.6 times the speed of light in avacuum.

The velocity of the microwave signal propagating through the paper pulpslurry is measure by the conductive effects of the slurry, in accordancewith the following equation:V=c*sqrt(E)

Where V is the velocity of the microwave signal propagating through theslurry, c is the speed of light in a vacuum, and E is the relativeconductivity of the material. Typical values of relative conductivityfor material comprising a paper/pulp slurry, for example, are:

-   -   Water relative conductivity=80;    -   Air relative conductivity=1; and    -   Fiber relative conductivity=3.

These meters typically work well in the absence of entrained air. Withentrained air present, the air displaces water and looks like additionalpulp fiber to the microwave meter. Thus, uncertainity in the amount ofentrained air translates directly into uncertainty in consistency.

SUMMARY OF THE INVENTION

Objects of the present invention include an apparatus having sensor fordetermining the speed of sound propagating within a pipe for determiningthe gas volume fraction of a process flow to correct the output of ameter for entrained gas, such as a volumetric flow meter and aconsistency meter.

According to the present invention, an apparatus for measuring aparameter of a process flow flowing within a pipe includes a first meterportion and a second meter portion. The first meter portion provides ameter measurement signal indicative of a parameter of the flowpropagating through the pipe. The second meter portion includes a sensorfor providing sound measurement signal indicative of the speed of soundpropagating within the pipe. A processor provides a compensated metermeasurement signal indicative of a measurement parameter corrected forentrained gas in the flow propagating through the pipe, in response tometer measurement signal and the sound measurement signal.

The foregoing and other objects, features and advantages of the presentinvention will become more apparent in light of the following detaileddescription of exemplary embodiments thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of an apparatus having an array ofsensors onto a pipe for measuring the volumetric flow and gas volumefraction of the mixture flowing in the pipe having entrained gas/airtherein, in accordance with the present invention.

FIG. 2 is a block diagram of an embodiment of the apparatus of FIG. 1,in accordance with the present invention.

FIG. 3 is a functional flow diagram of an apparatus embodying thepresent invention that compensates the volumetric flow measurement of avolumetric flow meter, in accordance with the present invention.

FIG. 4 is a block diagram of an apparatus for measuring the speed ofsound propagating through a process flow flowing within a pipe, inaccordance with the present invention.

FIG. 5 is a plot of Mixture Sound Speed as a function of gas volumefraction for a 5% consistency slurry over a range of process pressures,in accordance with the present invention.

FIG. 6 is a plot of Mixture Sound Speed a function of gas volumefraction for pure water and a 5% consistency slurry at 4 atm processpressure, in accordance with the present invention.

FIG. 7 is a plot of Mixture Sound Speed as a function of gas volumefraction for different consistency slurry over a range of processpressures, in accordance with the present invention.

FIG. 8 is a plot of Mixture Sound Speed a function of entrained airvolume fraction for slurry at a process pressure, in accordance with thepresent invention.

FIG. 9 is a K−w plot for acoustic field within 3 inch pipe containing˜2% air by volume entrained in water flowing 240 gpm, in accordance withthe present invention.

FIG. 10 is a cross-sectional view of a pipe having a turbulent pipeflowing having coherent structures therein, in accordance with thepresent invention.

FIG. 11 is a block diagram of an apparatus for measuring the vorticalfield of a process flow within a pipe, in accordance with the presentinvention.

FIG. 12 a kω plot of data processed from an apparatus embodying thepresent invention that illustrates slope of the convective ridge, and aplot of the optimization function of the convective ridge, in accordancewith the present invention.

FIG. 13 is a block diagram of an apparatus for measuring the vorticalfield and acoustic field of a process flow within a pipe, in accordancewith the present invention.

FIG. 14 is a block diagram of another apparatus for measuring thevortical field of a process flow within a pipe, in accordance with thepresent invention.

FIG. 15 is a functional flow diagram of an apparatus embodying thepresent invention that compensates the volumetric flow measurement of anelectromagnetic flow meter, in accordance with the present invention.

FIG. 16 is a functional flow diagram of an apparatus embodying thepresent invention that compensates the consistency measurement of aconsistency meter, in accordance with the present invention.

FIGS. 17–19 are configurations for an apparatus in accordance with thepresent invention.

FIGS. 20–22 are plots of the output of an apparatus embodying thepresent invention for compensating a microwave consistency meter, inaccordance with the present invention.

FIG. 23 is a block diagram of a closed loop system having a microwaveconsistency meter compensated for entrained gas, in accordance with thepresent invention.

FIG. 24 is a block diagram of a closed loop system having anelectromagnetic flow meter compensated for entrained gas, in accordancewith the present invention.

BEST MODE FOR CARRYING OUT THE INVENTION

Referring to FIG. 1, an apparatus, generally shown as 10, is provided tomeasure volumetric flow rate and gas volume fraction in liquids andmixtures (e.g. paper and pulp slurries or other solid liquid mixtures)having entrained gas therein (including air). The apparatus 10 inaccordance with the present invention determines the speed at whichsound propagates within a pipe 14 to measure entrained gas in liquidsand/or mixtures 12. To simplify the explanation of the present inventionthe flow propagating through the pipe will be referred to as a mixtureor slurry with the understanding that the flow may be a liquid or anyother mixture having entrained gas therein.

The following approach may be used with any technique that measures thesound speed of a fluid. However, it is particularly synergistic withsonar based volumetric flow meters such as described in U.S patentapplication Ser. No. 09/729,994, filed Dec. 4, 2000, now U.S. Pat. No.6,609,069, which are incorporated herein by reference, in that the soundspeed measurement, and thus gas volume fraction measurement, can beaccomplished using the same hardware as that required for the volumetricflow measurement. It should be noted, however, that the gas volumefraction measurement could be performed independently of a volumetricflow measurement, and would have utility as an important processmeasurement in isolation or in conjunction with other processmeasurements, which will be described in greater detail hereinafter.

FIG. 2 is a block diagram 1 of the apparatus 10 of FIG. 1 that includesa device 2 for measuring the speed of sound (SOS) propagating within apipe 14 and a device 3 for measuring the velocity of the mixture 12within the pipe 14. A pressure sensor 4 and/or temperature sensor 13measures the pressure and/or temperature of the mixture flowing throughthe pipe. Alternatively, the pressure and/or temperature may beestimated rather than actually measured. In response to the speed ofsound signal 5, the velocity 7 of the flow 12 and characteristics 6 ofthe flow (e.g., pressure and temperature), a processor 24 determines thegas volume fraction (GVF) of the flow 12, the uncompensated volumetricflow 9 of the mixture, and the volumetric flow 11 of the flowcompensated for the entrained air therein.

A flow chart 13 shown in FIG. 3 illustrates the function of theprocessor 24. As shown in FIG. 2, the inputs to the processor includesthe speed of sound (SOS) within the pipe 14, the velocity 7 of themixture 12, and the pressure and temperature 6 of the mixture. The fluidproperties of the mixture (e.g., SOS and density) are determined knowingthe pressure and temperature of the mixture. The gas volume fraction ofthe mixture (GVF) is determined using the SOS measurement and fluidproperties, which will be described in greater detail hereinafter. Thevolumetric flow rate of the mixture (including the entrained gas) isdetermined using the velocity and knowing the cross-sectional area ofthe inner diameter of the pipe. The processor 24 provides a compensatedvolumetric flow measurement of the mixture by correcting theuncompensated volumetric flow rate using the void fraction of the air.For example, correction for void fraction of gas may be as follows, fora no slip, homogeneous flow model:

Qair+Qliquid=Qmix

Qair=GVFair*Qmix

Qliquid=(1−GVFair)Qmix

Other models and corrections may be used to correct for gas volumefraction.

Other information relating to the gas volume fraction in a fluid and thespeed of sound (or sonic velocity) in the fluid, is described in “FluidMechanics and Measurements in two-phase flow Systems”, Institution ofmechanical engineers, proceedings 1969–1970 Vol. 184 part 3C, Sep. 24–251969, Birdcage Walk, Westminster, London S.W. 1, England, which isincorporated herein by reference.

FIG. 1 illustrates a schematic drawing of an embodiment of the presentinvention. The apparatus 10 includes a sensing device 16 comprising anarray of pressure sensors (or transducers) 18–21 spaced axially alongthe outer surface 22 of a pipe 14, having a process flow propagatingtherein. The pressure sensors measure the unsteady pressures produced byacoustical and vortical disturbances within the pipe, which areindicative of the SOS propagating through the pipe and the velocity ofthe mixture 12. The output signals (P₁–P_(N)) of the pressure sensors18–21 are provided to the processor 24, which processes the pressuremeasurement data and determines gas volume fraction (GVF), theuncompensated volumetric flow rate and the compensated volumetric flowrate, as described hereinbefore.

In an embodiment of the present invention shown in FIG. 1, the apparatus10 has at least four pressure sensors 18–21 disposed axially along thepipe 14 for measuring the unsteady pressure P₁–P_(N) of the mixture 12flowing therethrough. Both measurements are derive by interpreting theunsteady pressure field within the process piping using multipletransducers displaced axially over ˜2 diameters in length. The flowmeasurements can be performed using ported pressure transducers orclamp-on, strain-based sensors.

The apparatus 10 has the ability to measure the gas volume fraction andvolumetric flow rate using one or both of the following techniquesdescribed herein below:

-   -   1) Determining the speed of sound of acoustical disturbances or        sound waves propagating through the flow 12 using the array of        pressure sensors 18–21, and/or    -   2) Determining the velocity of vortical disturbances or “eddies”        propagating through the flow 12 using the array of pressure        sensors 18–21.

Generally, the first technique measures unsteady pressures created byacoustical disturbances propagating through the flow 12 to determine thespeed of sound (SOS) propagating through the flow. Knowing the pressureand/or temperature of the flow and the speed of sound of the acousticaldisturbances, the processing unit 24 can determine the gas volumefraction of the mixture, as described and shown in FIG. 3.

The apparatus in FIG. 1 also contemplates providing one or more acousticsources 27 to enable the measurement of the speed of sound propagatingthrough the flow for instances of acoustically quiet flow. The acousticsources may be a device that taps on and/or vibrates the wall of thepipe, for example. The acoustic sources may be disposed at the input endof output end of the array of sensors 18–21, or at both ends as shown.One should appreciate that in most instances the acoustics sources arenot necessary and the apparatus passively detects the acoustic ridgeprovided in the flow 12. The passive noise includes noise generated bypumps, valves, motors, and the turbulent mixture itself.

The second technique measures the velocities associated with unsteadyflow fields and/or pressure disturbances created by vorticaldisturbances or “eddies” 118 to determine the velocity of the flow 12.The pressure sensors 18–21 measure the unsteady pressures P₁–P_(N)created by the vortical disturbances as these disturbances convectwithin the flow 12 through the pipe 14 in a known manner, as shown inFIG. 10. Therefore, the velocity of these vortical disturbances isrelated to the velocity of the mixture and hence the volumetric flowrate may be determined, as will be described in greater detailhereinafter.

In one embodiment of the present invention as shown in FIG. 1, each ofthe pressure sensors 18–21 may include a piezoelectric film sensor tomeasure the unsteady pressures of the mixture 12 using either techniquedescribed hereinbefore.

The piezoelectric film sensors include a piezoelectric material or filmto generate an electrical signal proportional to the degree that thematerial is mechanically deformed or stressed. The piezoelectric sensingelement is typically conformed to allow complete or nearly completecircumferential measurement of induced strain to provide acircumferential-averaged pressure signal. The sensors can be formed fromPVDF films, co-polymer films, or flexible PZT sensors, similar to thatdescribed in “Piezo Film Sensors Technical Manual” provided byMeasurement Specialties, Inc., which is incorporated herein byreference. A piezoelectric film sensor that may be used for the presentinvention is part number 1-1002405-0, LDT4-028K, manufactured byMeasurement Specialties, Inc.

Piezoelectric film (“piezofilm”), like piezoelectric material, is adynamic material that develops an electrical charge proportional to achange in mechanical stress. Consequently, the piezoelectric materialmeasures the strain induced within the pipe 14 due to unsteady pressurevariations (e.g., vortical and/or acoustical) within the process mixture12. Strain within the pipe is transduced to an output voltage or currentby the attached piezoelectric sensor. The piezoelectrical material orfilm may be formed of a polymer, such as polarized fluoropolymer,polyvinylidene fluoride (PVDF). The piezoelectric film sensors aresimilar to that described in U.S. patent application Ser. No.10/712,833, which is incorporated herein by reference.

The apparatus 10 of the present invention may be configured andprogrammed to measure and process the detected unsteady pressuresP₁(t)–P_(N)(t) created by acoustic waves and/or vortical disturbances,respectively, propagating through the mixture to determine the SOSwithin the pipe 14 and the velocity of the mixture 12. One suchapparatus 110 is shown in FIG. 4 that measures the speed of sound (SOS)of one-dimensional sound waves propagating through the mixture todetermine the gas volume fraction of the mixture. It is known that soundpropagates through various mediums at various speeds in such fields asSONAR and RADAR fields. The speed of sound propagating through the pipeand mixture 12 may be determined using a number of known techniques,such as those set forth in U.S. patent application Ser. No. 09/344,094,entitled “Fluid Parameter Measurement in Pipes Using AcousticPressures”, filed Jun. 25, 1999, now U.S. Pat. No. 6,354,147; U.S.patent application Ser. No. 09/729,994, filed Dec. 4, 2002, now U.S.Pat. No. 6,609,069; U.S. patent application Ser. No. 09/997,221, filedNov. 28, 2001, now U.S. Pat. No. 6,587,798; and U.S. patent applicationSer. No. 10/007,749, entitled “Fluid Parameter Measurement in PipesUsing Acoustic Pressures”, filed Nov. 7, 2001, each of which areincorporated herein by reference.

In accordance with the present invention, the speed of sound propagatingthrough the mixture 12 is measured by passively listening to the flowwith an array of unsteady pressure sensors to determine the speed atwhich one-dimensional compression waves propagate through the mixture 12contained within the pipe 14.

As shown in FIG. 4, an apparatus 110 measuring the speed of sound in themixture 12 has an array of at least two acoustic pressure sensors115,116, located at two locations x₁,x₂ axially along the pipe 14. Onewill appreciate that the sensor array may include more than two pressuresensors as depicted by pressure sensors 117,118 at location, x₃,x_(N).The pressure generated by the acoustic waves may be measured throughpressure sensors 115–118. The pressure sensors 15–18 provide pressuretime-varying signals P₁(t),P₂(t),P₃(t),P_(N)(t) on lines 120,121,122,123to a signal processing unit 130 to known Fast Fourier Transform (FFT)logics 126,127,128,129, respectively. The FFT logics 126–129 calculatethe Fourier transform of the time-based input signals P₁(t)–P_(N)(t) andprovide complex frequency domain (or frequency based) signalsP₁(ω),P₂(ω),P₃(ω),P_(N)(ω) on lines 132,133,134,135 indicative of thefrequency content of the input signals. Instead of FFT's, any othertechnique for obtaining the frequency domain characteristics of thesignals P₁(t)–P_(N)(t), may be used. For example, the cross-spectraldensity and the power spectral density may be used to form a frequencydomain transfer functions (or frequency response or ratios) discussedhereinafter.

The frequency signals P₁(ω)–P_(N)(ω) are fed to array processing unit138 which provides a signal to line 40 indicative of the speed of soundof the mixture a_(mix) (discussed more hereinafter). The a_(mix) signalis provided to map (or equation) logic 142, which converts a_(mix) to apercent composition of a mixture and provides a % Comp signal to line 44indicative thereof (as discussed hereinafter).

More specifically, for planar one-dimensional acoustic waves in ahomogenous mixture, it is known that the acoustic pressure field P(x,t)at a location x along the pipe 14, where the wavelength λ of theacoustic waves to be measured is long compared to the diameter d of thepipe 14 (i.e., λ/d>>1), may be expressed as a superposition of a righttraveling wave and a left traveling wave, as follows:P(x,t)=(Ae ^(−ik) ^(r) ^(x) +Be ^(+ik) ^(l) ^(x))e ^(iωt)  Eq. 1where A,B are the frequency-based complex amplitudes of the right andleft traveling waves, respectively, x is the pressure measurementlocation along a pipe 14, ω is frequency (in rad/sec, where ω=2πf), andk_(r),k_(l) are wave numbers for the right and left traveling waves,respectively, which are defined as:

$\begin{matrix}{k_{r} \equiv {( \frac{\omega}{a_{mix}} )\frac{1}{1 + M_{x}}\mspace{14mu}{and}\mspace{14mu} k_{l}} \equiv {( \frac{\omega}{a_{mix}} )\frac{1}{1 - M_{x}}}} & {{Eq}.\mspace{14mu} 2}\end{matrix}$where a_(mix) is the speed of sound of the mixture in the pipe, ω isfrequency (in rad/sec), and M_(x) is the axial Mach number of the flowof the mixture within the pipe, where:

$\begin{matrix}{M_{x} \equiv \frac{V_{mix}}{a_{mix}}} & {{Eq}.\mspace{14mu} 3}\end{matrix}$where Vmix is the axial velocity of the mixture. For non-homogenousmixtures, the axial Mach number represents the average velocity of themixture and the low frequency acoustic field description remainssubstantially unaltered.

The data from the array of sensors 115–118 may be processed in anydomain, including the frequency/spatial domain, the temporal/spatialdomain, the temporal/wave-number domain or the wave-number/frequency(k−ω) domain. As such, any known array processing technique in any ofthese or other related domains may be used if desired, similar to thetechniques used in the fields of SONAR and RADAR.

One such technique of determining the speed of sound propagating throughthe flow 12 is using array processing techniques to define an acousticridge in the k−ω plane as shown in FIG. 9. The slope of the acousticridge is indicative of the speed of sound propagating through the flow12. This technique is similar to that described in U.S. Pat. No.6,587,798 filed Nov. 28, 2001, titled “Method and System for DeterminingThe Speed of Sound in a Fluid Within a Conduit”, which is incorporatedherein by reference. The speed of sound (SOS) is determined by applyingsonar arraying processing techniques to determine the speed at which theone dimensional acoustic waves propagate past the axial array ofunsteady pressure measurements distributed along the pipe 14.

The signal processor 24 performs a Fast Fourier Transform (FFT) of thetime-based pressure signals P₁(t)–P_(N)(t) to convert the pressuresignal into the frequency domain. The power of the frequency-domainpressure signals are then determined and defined in the k−ω plane byusing array processing algorithms (such as Capon and Music algorithms).The acoustic ridge in the k−ω plane, as shown in the k−ω plot of FIG. 9,is then determined. The speed of sound (SOS) is determined by measuringslope of the acoustic ridge. The gas volume fraction is then calculatedor otherwise determined, as described hereinafter.

The flow meter of the present invention uses known array processingtechniques, in particular the Minimum Variance, Distortionless Response(MVDR, or Capon technique), to identify pressure fluctuations, whichconvect with the materials flowing in a conduit and accurately ascertainthe velocity, and thus the flow rate, of said material. These processingtechniques utilize the covariance between multiple sensors 18–21 at aplurality of frequencies to identify signals that behave according to agiven assumed model; in the case of the apparatus 10, a model, whichrepresents pressure variations 20 convecting at a constant speed acrossthe pressure sensors comprising the flow meter monitoring head 12.

To calculate the power in the k−ω plane, as represent by a k−ω plot (seeFIG. 9) of either the pressure signals, the processor 58 determines thewavelength and so the (spatial) wavenumber k, and also the (temporal)frequency and so the angular frequency ω, of various spectral componentsof the acoustic waves created passively or actively within the pipe.There are numerous algorithms available in the public domain to performthe spatial/temporal decomposition of arrays of sensor units 18–21.

In the case of suitable acoustic pressures being present, the power inthe k−ω plane shown in a k−ω plot of FIG. 9 so determined will exhibit astructure that is called an acoustic ridge 61 associated with soundpropagating with the flow and one associated with sound propagatingagainst the flow. The acoustic ridge represents the concentration of thedisturbances that propagate with and against the flow and is amathematical manifestation of the relationship between the spatialvariations and temporal variations described above. Such a plot willindicate a tendency for k−ω pairs to appear more or less along a linewith some slope, the slope indicating the speed of sound traveling inboth directions, as is described in more detail below. The power in thek−ω plane so determined is then provided to a acoustic ridge identifier,which uses one or another feature extraction method to determine thelocation and orientation (slope) of any acoustic ridge present in thek−ω plane. Finally, information including the acoustic ridge orientation(slope) is used by an analyzer to determine the speed of sound.

The array processing unit 23 uses standard so-called beam forming, arrayprocessing, or adaptive array-processing algorithms, i.e. algorithms forprocessing the sensor signals using various delays and weighting tocreate suitable phase relationships between the signals provided by thedifferent sensors, thereby creating phased antenna array functionality.In other words, the beam forming or array processing algorithmstransform the time domain signals from the sensor array into theirspatial and temporal frequency components, i.e. into a set of wavenumbers given by k=2π/λ where λ is the wavelength of a spectralcomponent, and corresponding angular frequencies given by ω=2πν.

The prior art teaches many algorithms of use in spatially and temporallydecomposing a signal from a phased array of sensors, and the presentinvention is not restricted to any particular algorithm. One particularadaptive array processing algorithm is the Capon method/algorithm. Whilethe Capon method is described as one method, the present inventioncontemplates the use of other adaptive array processing algorithms, suchas MUSIC algorithm. The present invention recognizes that suchtechniques can be used to determine speed of sound propagating throughthe fluid 12.

Also, some or all of the functions within the processor 130 may beimplemented in software (using a microprocessor or computer) and/orfirmware, or may be implemented using analog and/or digital hardware,having sufficient memory, interfaces, and capacity to perform thefunctions described herein.

It is within the scope of the present invention that the pressure sensorspacing may be known or arbitrary and that as few as two sensors arerequired if certain information is known about the acoustic propertiesof the process flow 12. The pressure sensors are spaced sufficientlysuch that the entire length of the array (aperture) is at least asignificant fraction of the measured wavelength of the acoustic wavesbeing measured. The acoustic wavelength is a function of the type orcharacteristics of flow 12.

Based on the above discussion, one may use a short length scale apertureto measure the sound speed.

The characteristic acoustic length scale is: λ=c/f; where c is the speedof sound in a mixture, f is frequency and λ is wavelength.

If Aperture =L and if L/k is approx. constant.

Then Lwater/λwater=Lwater*f/C_(water)≈L_(GVF)*f/c_(GVF)

Therefore: L_(GVF)=Lwater (C_(GVF)/C_(water)); where GVF is gas volumefraction.

Thus for SOS of water (Cwater=5,000 ft/sec), and SOS of the Gas volumefraction (C GVF=500 ft/sec) and a length aperture of L water=5 ft (whichwe have shown is sufficient to accurately measure the SOS of water), thelength aperture for a gas volume fraction LGVF would be about 0.5 feet.

The entrained gas processing unit 25 assumes a nearly isothermalcondition for the flow 12. As such the gas volume fraction or the voidfraction is related to the speed of sound by the following quadraticequation:Ax ² +Bx+C=0

wherein x is the speed of sound, A=1+rg/rl*(K_(eff)/P−1)−K_(eff)/P,B=K_(eff)/P−2+rg/rl; C=1−K_(eff)/rl*a_(meas)^2); Rg=gas density,rl=liquid density, K_(eff)=effective K (modulus of the liquid andpipewall), P=pressure, and a_(meas)=measured speed of sound.

Effectively,Gas Voulume Fraction (GVF)=(−B+sqrt(B^2−4*A*C))/(2*A)

Alternatively, the sound speed of a mixture can be related to volumetricphase fraction (φ_(i)) of the components and the sound speed (a) anddensities (ρ) of the component through the Wood equation.

$\frac{1}{\rho_{mix}a_{{mix}_{\infty}}^{2}} = {{\sum\limits_{i = 1}^{N}\;{\frac{\phi_{i}}{\rho_{i}a_{i}^{2}}\mspace{31mu}{where}\mspace{14mu}\rho_{mix}}} = {\sum\limits_{i = 1}^{N}\;{\rho_{i}\phi_{i}}}}$

One dimensional compression waves propagating within a mixture 12contained within a pipe 14 exert an unsteady internal pressure loadingon the pipe. The degree to which the pipe displaces as a result of theunsteady pressure loading influences the speed of propagation of thecompression wave. The relationship among the infinite domain speed ofsound and density of a mixture; the elastic modulus (E), thickness (t),and radius (R) of a vacuum-backed cylindrical conduit; and the effectivepropagation velocity (a_(eff)) for one dimensional compression is givenby the following expression:

$\begin{matrix}{a_{eff} = \frac{1}{\sqrt{{1/a_{{mix}_{\infty}}^{2}} + {\rho_{mix}\frac{2R}{Et}}}}} & ( {{eq}\mspace{14mu} 1} )\end{matrix}$

Note: “vacuum backed” as used herein refers to a situation in which thefluid surrounding the pipe externally has negligible acoustic impedancecompared to that of the mixture internal to the pipe 14. For example,meter containing a typical water and pulp slurry immersed in air atstandard atmospheric conditions satisfies this condition and can beconsidered “vacuum-backed”.

The mixing rule essentially states that the compressibility of a mixture(1/(ρa²)) is the volumetrically-weighted average of thecompressibilities of the components. For gas/liquid mixtures 12 atpressure and temperatures typical of paper and pulp industry, thecompressibility of gas phase is orders of magnitudes greater than thatof the liquid. Thus, the compressibility of the gas phase and thedensity of the liquid phase primarily determine mixture sound speed.,and as such, it is necessary to have a good estimate of process pressureto interpret mixture sound speed in terms of volumetric fraction ofentrained air. The effect of process pressure on the relationshipbetween sound speed and entrained air volume fraction is shown in FIG.5.

Conversely, however, detailed knowledge of the liquid/slurry is notrequired for entrained air measurement. Variations in liquid density andcompressibility with changes in consistency have a negligible effect onmixture sound speed compared to the presence of entrained air. FIG. 6shows the mixture sound speed as a function of entrained air volumefraction for two slurries, one with 0% wood fiber and the other with 5%wood fiber by volume. As shown, the relationship between mixture soundspeed and gas volume fraction is essentially indistinguishable for thetwo slurries. Furthermore, mixture sound speed is shown to an excellentindicator of gas volume fraction, especially for the trace to moderateamounts of entrained air, from 0 to 5% by volume, typically encounteredin the paper and pulp industry.

For paper and pulp slurries, the conditions are such that for slurrieswith non-negligible amounts of entrained gas, say <0.01%, the complianceof standard industrial piping (Schedule 10 or 40 steel pipe) istypically negligible compared to that of the entrained air.

FIGS. 7 and 8 above show the relationship between sound speed andentrained air for slurries 12 with pulp contents representative of therange used in the paper and pulp industry. Referring to FIG. 7, twoslurry consistencies are shown; representing the lower limit, a purewater mixture is considered, and representing the higher end ofconsistencies, a 5% pulp/95% water slurry is considered. Since theeffect of entrained air on the sound speed of the mixture is highlysensitive to the compressibility of the entrained air, the effect of theentrained air is examined at two pressures, one at ambient representingthe lower limit of pressure, and one at 4 atmospheres representing atypical line pressure in a paper process. As shown, the consistency ofthe liquid slurry 12, i.e., the pulp content, has little effect on therelationship between entrained air volume fraction and mixture soundspeed. This indicates that an entrained air measurement could beaccurately performed, within 0.01% or so, with little or no knowledge ofthe consistency of the slurry. The chart does show a strong dependenceon line pressure. Physically, this effect is linked to thecompressibility of the air, and thus, this indicates that reasonableestimates of line pressure and temperature would be required toaccurately interpret mixture sound speed in terms of entrained air gasvolume fraction.

FIG. 7 also shows that for the region of interest, from roughly 1%entrained air to roughly 5% entrained air, mixture sound speeds (amix)are quite low compare to the liquid-only sound speeds. In this example,the sound speed of the pure water and the 5% pulp slurry werecalculated, based on reasonable estimates of the constituent densitiesand compressibilities, to be 1524 m/s and 1541 m/s, respectively. Thesound speed of these mixtures with 1% to 5% entrained air at typicaloperating pressure (1 atm to 4 atms) are on the order of 100 m/sec. Theimplication of these low sound speed is that the mixture sound speedcould be accurately determined with a array of sensors, ie using themethodology described in aforementioned U.S patent applications Ser. No.09/344,094, and/or Ser. No. 10/007,749, with an aperture that issimilar, or identical, to an array of sensors that would be suitable todetermine the convection velocity, using the methodology described inaforementioned U.S patent application, Ser. No. 10/007,736, which isincorporated herein by reference. Thus, performing a volumetric flowmeasurement and an entrained air volumetric flow measurement using theconvection velocity and mixture sound speed simultaneously, with thesame sensor array would provide functionality currently unavailable tothe paper and pulp industry.

For the sound speed measurement, the apparatus 110 utilizes similarprocessing algorithms as those employed for the volumetric flowmeasurement. As with convective disturbances (which is described ingreater detail hereinafter), the temporal and spatial frequency contentof sound propagating within the process piping is related through adispersion relationship.

$k = \frac{\omega}{a_{mix}}$

As before, k is the wave number, defined as k=2π/λ, ω is the temporalfrequency in rad/sec, and a_(mix) is the speed at which sound propagateswithin the process piping. Unlike disturbances, which convect with theflow, however, sound generally propagates in both directions, with andagainst the mean flow. For these cases, the acoustic power is locatedalong two acoustic ridges, one for the sound traveling with the flow ata speed of a_(mix)+V_(mix) and one for the sound traveling against theflow at a speed of a_(mix)−V_(mix).

FIG. 9 shows a k−ω plot generated for acoustic sound field recorded fromwater flowing at a rate of 240 gpm containing ˜2% entrained air byvolume in a 3 in, schedule 10, stainless steel pipe. The k−ω plot wasconstructed using data from an array of strain-based sensors attached tothe outside of the pipe. Two acoustic ridges are clearly evident. Basedon the slopes of the acoustic ridges, the sound speed for this for thismixture was 330 ft/sec (100 m/s), consistent with that predicted by theWood equation. Note that adding 2% air by volume reduces the sound speedof the bubbly mixture to less than 10% of the the sound speed of singlephase water.

While the sonar-based flow meter using an array of sensors to measurethe speed of sound of an acoustic wave propagating through the mixture,one will appreciate that any means for measuring the speed of sound ofthe acoustic wave may be used to determine the entrained air volumefraction of the mixture/fluid.

The apparatus 110 further includes the ability to measure of volumetricflow rate of the mixture by comparing the difference of the speed of onedimensional sound waves propagating with and against the mean flow.

This method of determining the volumetric flow rate of the flow 12relies on the interaction of the mean flow with the acoustic pressurefield. The interaction results in sound waves propagating with the meanflow traveling at the speed of sound (if the vapor/liquid mixture werenot flowing) plus the convection velocity and, conversely, sound wavestraveling against the mean flow propagating at the speed of sound minusthe convection velocity. That is,a _(R) =a _(mix) +ua _(L) =a _(mix) −uwhere a_(R)=velocity of a right traveling acoustic wave relative to astationary observer (i.e. the pipe 14), a_(L)=velocity of a lefttraveling acoustic wave apparent to a stationary observer, a_(mix)=speedof sound traveling through the mixture (if the mixture was not flowing)and u=the mean flow velocity (assumed to be flowing from left to rightin this instance). Combining these two equations yields an equation forthe mean velocity,

$u = \frac{a_{R} - a_{L}}{2}$Therefore, by measuring the propagation velocity of acoustic waves inboth directions relative to the pipe 14 as described hereinbefore, themean flow velocity can be calculated by multiplying the mean flowvelocity by the cross-sectional area of the pipe 14.

Further, FIG. 9 illustrates the ability of the present invention todetermine the velocity of a fluid moving in a pipe. The color contoursrepresent the relative signal power at all combinations of frequency andwavenumber. The highest power “ridges” represent the acoustic wave withslope of the ridges equal to the propagation speed. The dashed linesshow the best-fit two-variable maximization of the power with the twovariables being sound speed and flow velocity. The right-side ridgerepresents the acoustic wave traveling in the same direction as the bulkflow and therefore its slope is steeper than the left-side ridge thatrepresents the acoustic wave traveling in the opposite direction of theflow. This indicates that the acoustic wave traveling in the samedirection of the flow is traveling faster than the acoustic wavetraveling in the opposite direction of the flow relative to thestationary sensors located on the probe.

As discussed hereinbefore, the apparatus 10 of FIG. 1 embodying thepresent invention also includes the ability to measure volumetric flowrate of the mixture by measuring the unsteady pressures generated byvortical disturbances 188 propagating in the mixture 12 (see FIG. 10).The apparatus 10 uses one or both of the following techniques todetermine the convection velocity of the vortical disturbances withinthe process flow 12 by:

-   -   1) Characterizing the convective ridge of the vortical        disturbances using an array of unsteady pressure sensors.    -   2) Cross-correlating unsteady pressure variations using an array        of unsteady pressure sensors.

To measure volumetric flow, the sonar meter characterizes speed at whichcoherent vortical structures convect past an axial array of sensorsusing beam forming techniques developed over several decades forunderwater acoustic application. Coherent structures are an inherentfeature of turbulent boundary layers present in all turbulent flows.Unlike conventional vortex shedding meters, no internal geometry isrequired to generate these structures.

The overwhelming majority of industrial process flows involve turbulentflow 12. Turbulent fluctuations within the process flow govern many ofthe flow properties of practical interest including the pressure drop,heat transfer, and mixing. For engineering applications, consideringonly the time-averaged properties of turbulent flows is often sufficientfor design purposes. For sonar based array processing flow meteringtechnology, understanding the time-averaged velocity profile inturbulent flow 12 provides a means to interpret the relationship betweenspeed at which coherent structures 118 convect and the volumetricallyaveraged flow rate.

Turbulent pipe flows 12 are highly complex flows. Predicting the detailsof any turbulent flow is problematic, however, much is known regardingthe statistical properties of the flow. For instance, turbulent flowscontain self-generating, coherent vortical structures often termed“turbulent eddies”. The maximum length scale of these eddies is set bythe diameter of the pipe 14. These structures remain coherent forseveral tube diameters downstream, eventually breaking down intoprogressively smaller eddies until the energy is dissipated by viscouseffects.

Experimental investigations have established that eddies generatedwithin turbulent boundary layers convect at roughly 80% of maximum flowvelocity. For pipe flows, this implies that turbulent eddies willconvect at approximately the volumetrically averaged flow velocitywithin the pipe 14. The precise relationship between the convectionspeed of turbulent eddies and the flow rate for each class of meters canbe calibrated empirically as described below.

FIG. 10 illustrates the relevant flow features of turbulent pipe flow 12along with a axial array of sensors 18-21. As shown, the time-averagedaxial velocity is a function of radial position, from zero the wall to amaximum at the centerline of the pipe. The flow 12 near the wall ischaracterized by steep velocity gradients and transitions to relativelyuniform core flow near the center of the pipe 14. Vortical structures,often termed turbulent eddies, are superimposed over time averagedvelocity profile. These coherent structures contain temporally andspatially random fluctuations with magnitudes typically less than 10%percent of the mean flow velocity and are carried along with the meanflow. Experimental investigations have established that eddies generatedwithin turbulent boundary layers remain coherent for several pipediameters and convect at roughly 80% of maximum flow velocity(Schlichting, 1979).

From a volumetric flow measurement perspective, the volumetricallyaveraged flow velocity is of interest. The volumetrically averaged flowvelocity, defined as the total volumetric flow rate, Q, divided by thecross sectional area of the conduit, A, is a useful, but arbitrarilydefined property of the flow. In fact, given the velocity profile withinthe pipe, little flow is actually moving at this speed. The preciserelationship between the convection speed of turbulent eddies and theflow rate is determined experimentally through calibration for each.

The Reynolds number (Re), based on pipe diameter (D), characterizes manyof the engineering properties of the flow. The Reynolds number is anon-dimensional ratio representing the relative importance of inertialforces to viscous forces within a flow:

${Re} = {{\frac{inertial}{viscous}{forces}} = {\frac{\rho\; u\frac{\partial u}{\partial x}}{\mu\frac{\partial^{2}u}{\partial y^{2}}} = \frac{UD}{v}}}$Where ρ is the fluid density, μ is the dynamic viscosity, U is thevolumetrically averaged flow velocity and ν(=μ/ρ) is the kinematicviscosity.

The critical Reynolds number for pipe flows, above which flows areconsidered turbulent, is ˜2300. Most flows in the paper and pulpindustry have Reynolds number ranging from one hundred thousand toseveral million, well within the turbulent regime. In addition todemarcating a boundary between laminar and turbulent flow regimes, theReynolds number is a similarity parameter for pipe flows, i.e. flows ingeometrically similar pipes with the same Reynolds number aredynamically similar (Schlichting p.12).

The first technique of determining the convection velocity of thevortical disturbances within the flow 12 is by characterizing theconvective ridge of the vortical disturbances using an array of unsteadypressure sensors, similar to that shown in U.S. patent application Ser.No. 09/729,994, filed Dec. 4, 2000, entitled “Method and Apparatus forDetermining the Flow Velocity Within a Pipe”, which is incorporatedherein by reference.

The sonar flow metering methodology uses the convection velocity ofcoherent structure with turbulent pipe flows 12 to determine thevolumetric flow rate. The convection velocity of these eddies 188 isdetermined by applying sonar arraying processing techniques to determinethe speed at which the eddies convect past an axial array of unsteadypressure measurements distributed along the pipe 14, similar to thetechnique described for the apparatus 110 of FIG. 4 for measuring gasvolume fraction with a fluid.

The sonar-based algorithms determine the speed of the eddies 188 bycharacterizing both the temporal and spatially frequency characteristicsof the flow field. For a series of coherent eddies convecting past afixed array of sensors, the temporal and spatial frequency content ofpressure fluctuations are related through the following relationship:

$k = \frac{\omega}{U_{convect}}$Here k is the wave number, defined as k=2π/λ and has units of 1/length,ω is the temporal frequency in rad/sec, and U_(convect) is theconvection velocity. Thus, the shorter the wavelength (larger k) is, thehigher the temporal frequency.

In sonar array processing, the spatial/temporal frequency content oftime stationary sound fields are often displayed using “k−ω plots”, asdiscussed hereinbefore. K−ω plots are essentially three-dimensionalpower spectra in which the power of a sound field is decomposed intobins corresponding to specific spatial wave numbers and temporalfrequencies. On a k−ω plot, the power associated with a pressure fieldconvecting with the flow is distributed in regions, which satisfies thedispersion relationship developed above. This region is termed “theconvective ridge” 201 (Beranek, 1992) and the slope of this ridge on ak−w plot indicates the convective velocity of the pressure field. Thissuggests that the convective velocity of turbulent eddies, and henceflow rate within a pipe 14, can be determined by constructing a k−ω plotfrom the output of a phased array of sensor and identifying the slope ofthe convective ridge 201.

FIG. 12 shows an example of a k−ω plot generated from a phased array ofpressure sensors. The power contours show a well-defined convectiveridge. A parametric optimization method was used to determine the “best”line representing the slope of the convective ridge 201. For this case,a slope of 14.2 ft/sec was determined. The intermediate result of theoptimization procedure is displayed in the insert, showing thatoptimized value is a unique and well-defined optima.

The k−ω plot shown in FIG. 12 illustrates the fundamental principlebehind sonar based flow measure, namely that axial arrays of pressuresensors can be used in conjunction with sonar processing techniques todetermine the speed at which naturally occurring turbulent eddiesconvect within a pipe.

As shown in FIG. 11, the array processing unit 138 of the flow meter 210processes the input pressure signals P₁(ω)–P_(N)(ω) to define theconvective ridge 201 (see FIG. 12) in the k−ω plane. The slope of theridge determines the velocity of the aerated fluid or mixture 12. Avelocity processing determines the volumetric flow rate of the aeratedfluid 12 using the relationship of:Volumetric Flow Rate=Velocity(Cross-sectional Area of Pipe).

While two separate apparatus 110 and 211 may be used to measure the gasvolume fraction and velocity, respectively, of the fluid havingentrained gas therein to determine the compensated volumetric flow rate,the present invention contemplates a single array of sensors andprocessing unit may be used to perform both functions as suggestedhereinbefore. Such an apparatus 310 is shown in FIG. 13, wherein asingle array of pressure sensors 115–118 is used to determine both thespeed of sound within the fluid and the velocity of the fluid. A flowprocessing unit 312 that combines the functionality of the entrained airprocessing unit 142 of FIG. 4 and the velocity processing unit 213 ofFIG. 11 to provide a compensated volumetric flow measurement.

The present invention shown in FIGS. 1, 4, 11 and 13 contemplate thatoutput signals P₁( )–P_(N)( ) of adjacent signals may be differenced tofilter out common mode noise or acoustics to provide spatial filtering.Also, while the present invention shows an apparatus having two to foursensors to form an array, the present invention contemplates that arraymay includes any number of sensors, for example, arrays having between 2and sixteen sensors.

In the second technique, the apparatus 170 of FIG. 14 determines theconvection velocity of the vortical disturbances within the flow bycross correlating unsteady pressure variations using an array ofunsteady pressure sensors, similar to that shown in U.S. patentapplication Ser. No. 10/007,736, filed Nov. 8, 2001, entitled “Flow RateMeasurement Using Unsteady Pressures”, which is incorporated herein byreference.

Referring to FIG. 14, the apparatus 170 includes a sensing section 172along a pipe 14 and a signal processing unit 174. The pipe 14 has twomeasurement regions 176,178 located a distance ΔX apart along the pipe14. At the first measurement region 176 are two unsteady (or dynamic orac) pressure sensors 180,182, located a distance X₁ apart, capable ofmeasuring the unsteady pressure in the pipe 14, and at the secondmeasurement region 178, are two other unsteady pressure sensors 84,86,located a distance X₂ apart, capable of measuring the unsteady pressurein the pipe 14. Each pair of pressure sensors 180,182 and 184,186 act asspatial filters to remove certain acoustic signals from the unsteadypressure signals, and the distances X₁,X₂ are determined by the desiredfiltering characteristic for each spatial filter, as discussedhereinafter.

The apparatus 170 of the present invention measures velocitiesassociated with unsteady flow fields and/or pressure disturbancesrepresented by 188 associated therewith relating to turbulent eddies (orvortical flow fields), inhomogeneities in the flow, or any otherproperties of the flow, liquid, vapor, or pressure, having time varyingor stochastic properties that are manifested at least in part in theform of unsteady pressures. The vortical flow fields are generatedwithin the flow of the pipe 14 by a variety of non-discrete sources suchas remote machinery, pumps, valves, elbows, as well as the fluid ormixture flow itself. It is this last source, the fluid flowing withinthe pipe, that is a generic source of vortical flow fields primarilycaused by the shear forces between the flow 12 and the wall of the tubethat assures a minimum level of disturbances for which the presentinvention takes unique advantage. The flow generated vortical flowfields generally increase with mean flow velocity and do not occur atany predeterminable frequency. As such, no external discretevortex-generating source is required within the present invention andthus may operate using passive detection. It is within the scope of thepresent invention that the pressure sensor spacing may be known orarbitrary and that as few as two sensors are required if certaininformation is known about the acoustic properties of the system as willbe more fully described herein below.

The vortical flow fields 188 are, in general, comprised of pressuredisturbances having a wide variation in length scales and which have avariety of coherence length scales such as that described in thereference “Sound and Sources of Sound”, A. P.Dowling et al, HalstedPress, 1983, which is incorporated by reference to the extend ofunderstanding the invention. Certain of these vortical flow fields 188convect at or near, or related to the mean velocity of at least one ofthe elements within a mixture flowing through the pipe 14. The vorticalpressure disturbances 188 that contain information regarding convectionvelocity have temporal and spatial length scales as well as coherencelength scales that differ from other disturbances in the flow. Thepresent invention utilizes these properties to preferentially selectdisturbances of a desired axial length scale and coherence length scaleas will be more fully described hereinafter. For illustrative purposes,the terms vortical flow field and vortical pressure field will be usedto describe the above-described group of unsteady pressure fields havingtemporal and spatial length and coherence scales described herein.

Also, some or all of the functions within the signal processing unit 174may be implemented in software (using a microprocessor or computer)and/or firmware, or may be implemented using analog and/or digitalhardware, having sufficient memory, interfaces, and capacity to performthe functions described herein.

In particular, in the processing unit 174, the pressure signal P₁(t) onthe line 190 is provided to a positive input of a summer 200 and thepressure signal P₂(t) on the line 191 is provided to a negative input ofthe summer 200. The output of the summer 200 is provided to line 204indicative of the difference between the two pressure signals P₁,P₂(e.g., P₁–P₂=P_(as1)).

The pressure sensors 180,182 together with the summer 200 create aspatial filter 176. The line 204 is fed to bandpass filter 208, whichpasses a predetermined passband of frequencies and attenuatesfrequencies outside the passband. In accordance with the presentinvention, the passband of the filter 208 is set to filter out (orattenuate) the dc portion and the high frequency portion of the inputsignals and to pass the frequencies therebetween. Other passbands may beused in other embodiments, if desired. Passband filter 208 provides afiltered signal P_(asf)1 on a line 212 to Cross-Correlation Logic 216,described hereinafter.

The pressure signal P₃(t) on the line 192 is provided to a positiveinput of a summer 202 and the pressure signal P₄(t) on the line 193 isprovided to a negative input of the summer 202. The pressure sensors83,84 together with the summer 202 create a spatial filter 178. Theoutput of the summer 202 is provided on a line 206 indicative of thedifference between the two pressure signals P₃,P₄ (e.g., P₃–P₄=P_(as2)).The line 206 is fed to a bandpass filter 210, similar to the bandpassfilter 108 discussed hereinbefore, which passes frequencies within thepassband and attenuates frequencies outside the passband. The filter 210provides a filtered signal P_(asf)2 on a line 214 to theCross-Correlation Logic 216. The signs on the summers 200,202 may beswapped if desired, provided the signs of both summers are swappedtogether. In addition, the pressure signals P₁,P₂,P₃,P₄ may be scaledprior to presentation to the summers 200,202.

The Cross-Correlation Logic 216 calculates a known time domaincross-correlation between the signals P_(asf1) and P_(asf2) on the lines212,214, respectively, and provides an output signal on a line 218indicative of the time delay τ it takes for an vortical flow field 188(or vortex, stochastic, or vortical structure, field, disturbance orperturbation within the flow) to propagate from one sensing region 176to the other sensing region 178. Such vortical flow disturbances, as isknown, are coherent dynamic conditions that can occur in the flow whichsubstantially decay (by a predetermined amount) over a predetermineddistance (or coherence length) and convect (or flow) at or near theaverage velocity of the fluid flow. As described above, the vorticalflow field 188 also has a stochastic or vortical pressure disturbanceassociated with it. In general, the vortical flow disturbances 188 aredistributed throughout the flow, particularly in high shear regions,such as boundary layers (e.g., along the inner wall of the tube 14) andare shown herein as discrete vortical flow fields 188. Because thevortical flow fields (and the associated pressure disturbance) convectat or near the mean flow velocity, the propagation time delay τ isrelated to the velocity of the flow by the distance ΔX between themeasurement regions 176,178, as discussed hereinafter.

The present invention uses temporal and spatial filtering toprecondition the pressure signals to effectively filter out the acousticpressure disturbances P_(acoustic) and other long wavelength (comparedto the sensor spacing) pressure disturbances in the tube 14 at the twosensing regions 176,178 and retain a substantial portion of the vorticalpressure disturbances P_(vortical) associated with the vortical flowfield 188 and any other short wavelength (compared to the sensorspacing) low frequency pressure disturbances P_(other). In accordancewith the present invention, if the low frequency pressure disturbancesP_(other) are small, they will not substantially impair the measurementaccuracy of P_(vorical).

Another embodiment of the present invention includes a pressure sensorsuch as pipe strain sensors, accelerometers, velocity sensors ordisplacement sensors, discussed hereinafter, that are mounted onto astrap to enable the pressure sensor to be clamped onto the pipe. Thesensors may be removable or permanently attached via known mechanicaltechniques such as mechanical fastener, spring loaded, clamped, clamshell arrangement, strapping or other equivalents. These certain typesof pressure sensors, it may be desirable for the pipe 12 to exhibit acertain amount of pipe compliance.

Instead of single point pressure sensors 18–21, at the axial locationsalong the pipe 12, two or more pressure sensors may be used around thecircumference of the pipe 12 at each of the axial locations. The signalsfrom the pressure sensors around the circumference at a given axiallocation may be averaged to provide a cross-sectional (or circumference)averaged unsteady acoustic pressure measurement. Other numbers ofacoustic pressure sensors and annular spacing may be used. Averagingmultiple annular pressure sensors reduces noises from disturbances andpipe vibrations and other sources of noise not related to theone-dimensional acoustic pressure waves in the pipe 12, thereby creatinga spatial array of pressure sensors to help characterize theone-dimensional sound field within the pipe 12.

The pressure sensors 18–21 of FIG. 1 described herein may be any type ofpressure sensor, capable of measuring the unsteady (or ac or dynamic )pressures within a pipe 14, such as piezoelectric, optical, capacitive,resistive (e.g., Wheatstone bridge), accelerometers (or geophones),velocity measuring devices, displacement measuring devices, etc. Ifoptical pressure sensors are used, the sensors 18–21 may be Bragggrating based pressure sensors, such as that described in U.S. patentapplication Ser. No. 08/925,598, entitled “High Sensitivity Fiber OpticPressure Sensor For Use In Harsh Environments”, filed Sep. 8, 1997, nowU.S. Pat. No. 6,016,702, and in U.S. patent application Ser. No.10/224,821, entitled “Non-Intrusive Fiber Optic Pressure Sensor forMeasuring Unsteady Pressures within a Pipe”, which are incorporatedherein by reference. In an embodiment of the present invention thatutilizes fiber optics as the pressure sensors 14 they may be connectedindividually or may be multiplexed along one or more optical fibersusing wavelength division multiplexing (WDM), time division multiplexing(TDM), or any other optical multiplexing techniques.

In certain embodiments of the present invention, a piezo-electronicpressure transducer may be used as one or more of the pressure sensors15–18 and it may measure the unsteady (or dynamic or ac) pressurevariations inside the tube 14 by measuring the pressure levels inside ofthe tube. These sensors may be ported within the pipe to make directcontact with the mixture 12. In an embodiment of the present invention,the sensors 14 comprise pressure sensors manufactured by PCBPiezotronics. In one pressure sensor there are integrated circuitpiezoelectric voltage mode-type sensors that feature built-inmicroelectronic amplifiers, and convert the high-impedance charge into alow-impedance voltage output. Specifically, a Model 106B manufactured byPCB Piezotronics is used which is a high sensitivity, accelerationcompensated integrated circuit piezoelectric quartz pressure sensorsuitable for measuring low pressure acoustic phenomena in hydraulic andpneumatic systems. It has the unique capability to measure smallpressure changes of less than 0.001 psi under high static conditions.The 106B has a 300 mV/psi sensitivity and a resolution of 91 dB (0.0001psi).

The pressure sensors incorporate a built-in MOSFET microelectronicamplifier to convert the high-impedance charge output into alow-impedance voltage signal. The sensor is powered from aconstant-current source and can operate over long coaxial or ribboncable without signal degradation. The low-impedance voltage signal isnot affected by triboelectric cable noise or insulationresistance-degrading contaminants. Power to operate integrated circuitpiezoelectric sensors generally takes the form of a low-cost, 24 to 27VDC, 2 to 20 mA constant-current supply. A data acquisition system ofthe present invention may incorporate constant-current power fordirectly powering integrated circuit piezoelectric sensors.

Most piezoelectric pressure sensors are constructed with eithercompression mode quartz crystals preloaded in a rigid housing, orunconstrained tourmaline crystals. These designs give the sensorsmicrosecond response times and resonant frequencies in the hundreds ofkHz, with minimal overshoot or ringing. Small diaphragm diameters ensurespatial resolution of narrow shock waves.

The output characteristic of piezoelectric pressure sensor systems isthat of an AC-coupled system, where repetitive signals decay until thereis an equal area above and below the original base line. As magnitudelevels of the monitored event fluctuate, the output remains stabilizedaround the base line with the positive and negative areas of the curveremaining equal.

It is also within the scope of the present invention that any strainsensing technique may be used to measure the variations in strain in thepipe, such as highly sensitive piezoelectric, electronic or electric,strain gages and piezo-resistive strain gages attached to the pipe 12.Other strain gages include resistive foil type gages having a race trackconfiguration similar to that disclosed U.S. patent application Ser. No.09/344,094, filed Jun. 25, 1999, now U.S. Pat. No. 6,354,147, which isincorporated herein by reference. The invention also contemplates straingages being disposed about a predetermined portion of the circumferenceof pipe 12. The axial placement of and separation distance ΔX₁, ΔX₂between the strain sensors are determined as described herein above.

It is also within the scope of the present invention that any otherstrain sensing technique may be used to measure the variations in strainin the tube, such as highly sensitive piezoelectric, electronic orelectric, strain gages attached to or embedded in the tube 14.

The present invention also contemplates the sensors 18–21 may beultra-sonic sensors, especially, for measuring the vortical disturbancesto determine the velocity of the flow, similar to that described in U.S.patent application Ser. No. 10/756,977, filed on Jan. 13, 2004, which isincorporated herein by reference.

Note that this entrained air or gas volume fraction measurement GVFgas 8may be used with any flow meter to correct for errors introduced into ameasurement by entrained air. For instance, an electromagnetic flowmeter will show an error when entrained air exists in the mixture. Thepresent invention may be used to correct for this error.

Referring to 15, the present invention contemplates an apparatus 300 forproviding a volumetric flow measurement 11 that is compensated forentrained gas/air in the liquid or mixture 12. The apparatus 300includes a device 302 for measuring the gas volume fraction of themixture, which is substantially similar to that described herein before,and an electromagnetic flow meter 304 (also know as a Magmeter) formeasuring the uncompensated volumetric flow rate of the mixture 12within the pipe 14. As shown, the GVF device 302 provides a signal 8indicative of the gas volume fraction of the mixture 12 to theelectromagnetic flow meter 304. The magmeter 304 then compensates (orcorrects) volumetric flow measurement 308 for entrained gas/air inresponse to the gas volume fraction signal 8. For example, this can beaccomplished in accordance with the following equation:Compensated Vol. Flow Rate=Vol. Flow Rate (1−Gas Volume Fraction)

The electromagnetic flow meter 308 may comprise an electromagnetic flowmeter as described hereinbefore, such as that 8700 Series Magmetermanufactured by Rosemount. However, one will appreciate that theentrained air meter portion may used to compensate or correct anyvolumetric flow meter that is able to provide a volumetric flow metermeasurement.

While the gas volume fraction signal 8 was provided to the magmeter 304to compensate the volumetric flow rate, the invention contemplates thatthe correction for entrained gas/air may be performed in the GVF device302.

Similarly, this GVF device 302 for measuring entrained air or gas volumefraction measurement GVFair 8 may be used with any consistency meter tocorrect for errors introduced into a measurement by entrained gas/air.For instance, a consistency meter will show an error when entrained airexists in the mixture. The present invention may be used to correct forthis error.

Referring to 14, the present invention contemplates an apparatus 400 forproviding a consistency measurement 11 that is compensated for entrainedgas/air in the mixture or slurry 12 (e.g. paper/pulp slurry). Theapparatus 300 includes a device 302 for measuring the gas volumefraction of the slurry 12, which is substantially similar to thatdescribed herein before, and a consistency meter 402 for measuring theuncompensated consistency measurement of the mixture 12 within the pipe14. As shown, the GVF device 302 provides a signal 8 indicative of thegas volume fraction of the slurry 12 to the consistency meter 402. Theconsistency 402 then compensates (or corrects) consistency measurement404 for entrained gas/air in response to the gas volume fraction signal8. For example, this can be accomplished in accordance with thefollowing equation:Cmixture=Uncompensated Consistency Measurement−(1.4)(GVFair)

The consistency meter 402 may comprise a microwave consistency meter asdescribed hereinbefore, such as that 8700 Series Magmeter manufacturedby Rosemount. However, one will appreciate that the consistency meterportion may used to compensate or correct any consistency meter that isable to provide a consistency measurement.

While the gas volume fraction signal 8 was provided to the consistencymeter 402 to compensate the consistency measurement as shown in FIGS.16, the invention contemplates that the correction for entrained gas/airmay be performed in the GVF device 302. Referring to FIG. 17, thepresent invention contemplates the consistency meter 402 in accordancewith the present invention receives and processes the measured pressureinput 6 and the gas volume fraction input 8 (compensated for pressure)to provide a corrected consistency output 406 to the plant DCS 410.

In FIG. 18, the plant DCS 410 in accordance with the present inventionreceives and process the uncorrected consistency measurement 404 fromthe consistency meter 402 and a GVF input 8 (compensated for pressure)and provides a corrected consistency output 406. In FIG. 19, the plantDCS 410 in accordance with the present invention receives and processesan uncorrected consistency measurement, a pressure measurement, and GVFmeasurement and provides a corrected consistency measurement 406 and aGVF measurement (compensated for process pressure).

FIGS. 20–22 show data from an apparatus 400 in accordance with thepresent invention that measured and corrected for entrained air within aslurry propagating through a pipe. FIG. 20 shows the measuredconsistency from a consistency meter 402, the measured GVFair for a GVFmeter 302 and the corrected consistency 406 over an eight hour timeperiod. FIG. 21 shows the measured consistency from a consistency meter402, the measured GVFair for a GVF meter 302 and the correctedconsistency 406 for a slurry having macro-bubbles flowing therein. FIG.22 shows the measured consistency from a consistency meter 402, themeasured GVFair for a GVF meter 302 and the corrected consistency 406for a slurry having micro-bubbles flowing therein. Consequently, asshown, the present invention eliminates the big bubble/small bubbleanalysis/compensation that other flow meters attempt to do tocompensation for entrained gas/air in the process flow 12.

Microwave consistency analyzers (MCA) are commonly used in the papermaking industry as the sensing element in a feedback loop designedmaintain a preset consistency level within flow lines. The output of theMCA is used to control the mixing ratio between, typically, thick stocklines and dilution lines.

As developed previously, MCA rely on a “Speed of Light” measurement todetermine the consistency of a pulp and water slurry. In the absence ofentrained air, MCA meters are considered the most accurate consistencymeasuring devices available. However, using an MCA to control theconsistency of approach lines in the presence of entrained air can beproblematic. MCAs over-estimate consistency in the presence of entrainedair. MCAs can over estimate the consistency of a pulp slurries byapproximately 1.4 times the GVF in percent.

For processes that use MCAs to control consistency, the overestimate ofconsistency in the presence of entrained air can have direct impact onpaper sheet strength and therefore paper breaks in the paper makingprocess. Slurry consistency and entrained air each have an impact onpaper strength and quality. In general, reducing consistency orincreasing entrained air levels degrade the strength of the paper. Thus,for system controlling based on the output of a MCA, an unobservedincrease in the entrained air will have a compounded effect on the paperquality. If unrecognized, the control system will see the increase inentrained air as an increase in measured consistency. The control loopwill then increase the dilution water in an attempt maintain (i.e.lower) the measured consistency. Unfortunately, this action has theresult of reducing the actual consistency to below intended levelsduring the periods of higher than average entrained air. The more theentrained air, the greater the problem becomes. This unintended couplingbetween entrained air and actual fiber content can lead to problems.

The problems posed by the coupling of entrained air and actualconsistency in systems control with MCA can be further aggrevated if thesource of the entrained air is in the dilution water.

FIG. 23 illustrates a control loop 400 for controlling the consistencyof a pulp and paper slurry, for example, having a mixing valve 404 formixing a liquid into the process flow and a mixing valve 404 for mixingpulp into the process flow 12. A microwave consistency analyzer (ormeter) 410 and a gas volume fraction meter 412, similar to that shown inFIG. 4, provide respective uncompensated consistency signal and gasvolume fraction signal to a controller 406. The controller determinesthe compensated consistency measurement in light of the entrained gas inthe process flow 12. In response to the compensated consistencymeasurement, the controller 406 provides respective control signals 408to the mixing valves 402,404 to ensure the consistency of the processflow 12 is maintained within a predetermined range. While the controllerincludes the processing of the data from the MCA and the GVF meter todetermine compensated consistency, the invention contemplates that theGVF meter or MCA may process the data to determine the compensatedconsistency measurement, similar to that described hereinbefore.

Similarly, as shown in FIG. 24, a control loop 500 that includes amagmeter 510 and GVF meter 512, similar to that shown in FIG. 4, toprovide a measurement of the flow rate of the process flow 12 and thegas volume fraction of the process flow, respectively. A controller 506receives the data from the magmeter and the GVF meter and determines thecompensated flow rate in light of the entrained gas in the process flow12. In response to the flow rate measurement, the controller 506provides a control signal 508 to a pump 502 to ensure the flow rate ofthe process flow 12 is maintained within a predetermined range. Whilethe controller 506 includes processing the data from the magmeter 510and the GVF meter 512 to determine the compensated flow rate, theinvention contemplates that the GVF meter or flow meter may process thedata to determine the compensated volumetric flow rate measurement,similar to that described hereinbefore.

While the control loops of FIGS. 23 and 24 show a microwave consistencymeter and a magmeter, respectively, using a meter to measure the gasvolume fraction to compensate for entrained gas within the flow, thepresent invention contemplates that the gas volume fraction meter can beused with any meter that measures a parameter of the flow that is effectby entrained gas in a flow loop.

It should be understood that any of the features, characteristics,alternatives or modifications described regarding a particularembodiment herein may also be applied, used, or incorporated with anyother embodiment described herein.

Although the invention has been described and illustrated with respectto exemplary embodiments thereof, the foregoing and various otheradditions and omissions may be made therein and thereto withoutdeparting from the spirit and scope of the present invention.

1. An apparatus for measuring a parameter of a process flow flowingwithin a pipe, the apparatus comprising: a first meter including asensor that provides a measurement signal indicative of a parameter ofthe flow propagating through the pipe; a second meter including a sensorthat provides a sound measurement signal indicative of the speed ofsound propagating through the process flow; and a processor thatdetermines a compensated measurement signal indicative of themeasurement signal compensated for entrained gas in the process flow, inresponse to the measurement signal and the sound measurement signal. 2.The apparatus of claim 1, wherein the second meter includes at least twostrain sensors disposed at different axial locations along the pipe,each of the strain sensors providing a respective strain signalindicative of acoustic pressure disturbances within the pipe at acorresponding axial position, wherein the second meter, responsive tosaid pressure signals, provides the sound measurement signal.
 3. Theapparatus of claim 2, wherein the second meter determines the slope ofan acoustic ridge in the k−ω plane to determine the sound measurementsignal.
 4. The apparatus of claim 1, wherein the first meter includes atleast two strain sensors at different axial locations along the pipe,each of the strain sensors providing a respective strain signalindicative of unsteady pressure disturbances within the pipe at acorresponding axial position, wherein the first meter, responsive tosaid strain signals, provides a signal indicative of a parameter of theprocess flow flowing within the pipe.
 5. The apparatus of claim 4,wherein the parameter of the process flow is one of velocity of theprocess flow and/or the volumetric flow of the process flow.
 6. Theapparatus of claim 4, wherein the first meter determines the slope of aconvective ridge in the k−ω plane to determine the velocity of theprocess flow flowing in the pipe.
 7. The apparatus of claim 4, whereinthe unsteady pressure disturbances are vortical pressure disturbances.8. The apparatus of claim 4, wherein the strain signals indicative areindicative of the velocity of the process flow through the pipe.
 9. Theapparatus of claim 1, wherein the first meter is a volumetric flow meterand the measurement signal is indicative of the volumetric flow rate ofthe process flow.
 10. The apparatus of claim 9, wherein the volumetricflow meter is an electromagnetic flow meter.
 11. The apparatus of claim1, wherein the first meter is a consistency flow meter and themeasurement signal is indicative of the consistency of the process flow.12. The apparatus of claim 11, wherein the consistency meter is amicrowave consistency meter.
 13. The apparatus of claim 1, wherein thesecond meter provides a signal indicative of the gas volume fraction ofthe process flow in response to the sound signal measurement.
 14. Theapparatus of claim 13, wherein the gas volume fraction is determinedusing the following formula:Gas Voulume Fraction=−B+sqrt(B^2−4*A*C))/(2*A) whereinA=1+rg/rl*(K_(eff)/P−1)−K_(eff)/P, B=K_(eff)P−2+rg/rl;C=1−K_(eff)/rl*a_(meas)^2; Rg=gas density, rl=liquid density,K_(eff)=effective K (modulus of the liquid and pipewall), P=pressure,and a_(meas)=measured speed of sound.
 15. The apparatus of claim 1,wherein the compensated measurement signal is indicative of thevolumetric flow rate of the non-aerated portion of the process flow. 16.The apparatus of claim 14, wherein the compensated measurement signal isdetermine by Q_(comp)=Q_(meas)(1−φ), where Q_(comp) is the compensatedmeasurement signal, Q_(meas) is the measurement signal, and φ is the gasvolume fraction of the process flow.
 17. The apparatus of claim 1,wherein the measurement signal is indicative of the consistency of theprocess flow flowing in the pipe.
 18. The apparatus of claim 1, whereinthe compensated measurement signal is indicative of the consistency ofthe non-aerated portion of the process flow.
 19. The apparatus of claim18, wherein the compensated measurement signal is determine byQ_(comp)=Q_(meas)(1−Rφ), where Q_(comp) is the compensated measurementsignal, Q_(meas) is the measurement signal, R is a compensation factor,and φ is the gas volume fraction of the process flow.
 20. The apparatusof claim 19, wherein the compensation factor is approximately 1.4. 21.The apparatus of claim 1, wherein the process flow is one of a liquidhaving entrained gas, a mixture having entrained gas, a liquid-liquidmixture having entrained gas, a liquid-solid mixture having entrainedgas, and a slurry having entrained gas.
 22. The apparatus of claim 1,wherein the first meter and second meter have at least one commonsensor.
 23. The apparatus of claim 1, wherein the second meter measuresthe speed of an one dimensional acoustic wave propagating through theprocess flow.
 24. The apparatus of claim 1, wherein the second metermeasures the speed of an acoustic wave propagating axially through theprocess flow in the pipe.
 25. The apparatus of claim 1, wherein thesecond meter includes 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, or 16sensors disposed at different axial locations along the pipe, each ofthe strain sensors providing a respective strain signal indicative ofacoustic pressure disturbances within the pipe at a corresponding axialposition, wherein the second meter, responsive to said pressure signals,provides the sound measurement signal.
 26. The apparatus of claim 25,wherein the apparatus further includes at least one of a pressure sensorand temperature sensor to respective determine the pressure andtemperature of the process flow.
 27. The apparatus of claim 1, whereinthe processor determines the gas volume fraction of the process flow inresponse to the sound measurement signal and at least one of thepressure and temperature of the process flow.
 28. A method for measuringa parameter of a process flow flowing within a pipe, the methodcomprising: receiving a measurement signal indicative of a parameter ofthe process flow propagating through the pipe; receiving a soundmeasurement signal indicative of the speed of sound propagating theprocess flow; and determining a compensated measurement signalindicative of the measurement signal compensated for entrained gas inthe process flow, in response to the measurement signal and the soundmeasurement signal.
 29. The method of claim 28, further including;measuring the parameter of the process flow propagating through thepipe, and providing the measurement signal; and measuring the speed ofsound propagating the process flow, and providing the sound measurementsignal.
 30. The method of claim 28, further includes determining asignal indicative of the gas volume fraction of the process flow inresponse to the sound signal measurement.
 31. The method of claim 30,wherein the gas volume fraction is determined using the followingformula:Gas Voulume Fraction=−B+sqrt(B^2−4*A*C))/(2*A) whereinA=1+rg/rl*(K_(eff)/P−1)−K_(eff)/P, B=K_(eff)P−2+rg/rl;C=1−K_(eff)/rl*a_(meas)^2; Rg=gas density, rl=liquid density,K_(eff)=effective K (modulus of the liquid and pipewall), P=pressure,and a_(meas)=measured speed of sound.
 32. The method of claim 28,wherein the measurement signal is indicative of the volumetric flow rateof the process flow flowing in the pipe.
 33. The method of claim 32,wherein the compensated measurement signal is indicative of thevolumetric flow rate of the non-aerated portion of the process flow. 34.The method of claim 33, wherein the compensated measurement signal isdetermined by Q_(comp) 32 Q_(meas)(1−φ), where Q_(comp) is thecompensated measurement signal, Q_(meas) is the measurement signal, andφ is the gas volume fraction of the process flow.
 35. The method ofclaim 28, wherein the measurement signal is indicative of theconsistency of the process flow flowing in the pipe.
 36. The method ofclaim 35, wherein the compensated measurement is indicative of theconsistency of the non-aerated portion of the process flow.
 37. Themethod of claim 36, wherein the compensated measurement signal isdetermined by Q_(comp)=Q_(meas)(1−Rφ), where Q_(comp) is the compensatedmeasurement signal, Q_(meas) is the measurement signal, R is acompensation factor and φ is the gas volume fraction of the processflow.
 38. The apparatus of claim 37, wherein the compensation factor isapproximately 1.4.
 39. The method of claim 28, wherein the process flowis one of a liquid having entrained gas, a mixture having entrained gas,a liquid-liquid mixture having entrained gas, a liquid-solid mixturehaving entrained gas, and a slurry having entrained gas.
 40. The methodof claim 28, wherein the measurement signal is indicative of thevolumetric flow rate of the process flow which is provided by avolumetric flow meter.
 41. The method of claim 40, wherein thevolumetric flow meter is an electromagnetic flow meter.
 42. The methodof claim 28, wherein the measurement signal is indicative of theconsistency of the process flow which is provided by a consistencymeter.
 43. The method of claim 42, wherein the consistency meter is amicrowave consistency meter.
 44. The method of claim 28, wherein thesound measurement signal is provided by a meter that includes at leasttwo strain sensors disposed at different axial locations along the pipe,each of the strain sensors providing a respective strain signalindicative of an acoustic pressure disturbance within the pipe at acorresponding axial position.
 45. The method of claim 44, furtherincludes determining a signal indicative of the gas volume fraction ofthe process flow in response to the sound measurement signal.
 46. Themethod of claim 44, further includes determining the slope of anacoustic ridge in the k−ω plane to determine the sound measurementsignal.
 47. The method of claim 28, wherein the measurement signal isprovided by a meter that includes at least two strain sensors atdifferent axial locations along the pipe, each of the strain sensorsproviding a respective strain signal indicative of unsteady pressuredisturbances within the process flow flowing in the pipe at acorresponding axial position, wherein the meter, responsive to saidstrain signals, provides a signal indicative of a parameter of theprocess flow flowing within the pipe.
 48. The method of claim 47,wherein the parameter of the process flow is one of velocity of theprocess flow and/or the volumetric flow of the process flow.
 49. Themethod of claim 47, further includes determining the slope of aconvective ridge in the k−ω plane to determine the velocity of theprocess flow flowing in the pipe.
 50. The method of claim 47, whereinthe unsteady pressure disturbances are vortical pressure disturbances.51. The apparatus of claim 47, wherein the strain signals indicative areindicative of the velocity of the process flow through the pipe.
 52. Themethod of claim 28, wherein the measurement signal and the soundmeasurement signal are determined from a sensed signal from at least onecommon sensor disposed at a location of the pipe.
 53. The method ofclaim 28, wherein the sound measurement signal is indicative of thespeed of a one dimensional acoustic wave propagating through the processflow.
 54. The method of claim 28, wherein the sound measurement signalis provided by a meter includes 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,15, or 16 sensors disposed at different axial locations along the pipe,each of the strain sensors providing a respective strain signalindicative of acoustic pressure disturbances within the pipe at acorresponding axial position, wherein the meter, responsive to saidpressure signals, provides the sound measurement signal.
 55. The methodof claim 28, further includes determining the gas volume fraction inresponse to the sound measurement signal and at least one of a pressuresignal and temperature signal of the process flow indicative of thepressure and temperature, respectively, of the process flow.
 56. Themethod of claim 55, wherein the pressure signal and/or temperaturesignal is provided by a respective pressure sensor and temperaturesensor.
 57. An apparatus for measuring a parameter of a process flowflowing within a pipe, the apparatus comprising: a first means forproviding a measurement signal indicative of a parameter of the flowpropagating through the pipe; a second means for providing a soundmeasurement signal indicative of the speed of sound propagating throughthe process flow; and a third means for determining a compensatedmeasurement signal indicative of the measurement signal compensated forentrained gas in the process flow, in response to the measurement signaland the sound measurement signal.